burning-half-the-deck problem

[Big kicker]

[ QUOTE ]
I remove the bottom card of the deck. What are the odds now?? 2/49, she replies. D'OH!!!!!

[/ QUOTE ]

Just keep burning one card at the time - when there is only two cards left she will have a problem.

[Flow73]

[ QUOTE ]

We breakdown the problem but we differ in some aspects. She thinks that the burn card, for example, might be an Ace, or a trey, or a King, and therefore is changing our odds and probabilities. I explain to her that if we knew what that card was she would definately be correct. But we do not know and therefore can only attempt to calculate the likelyhood that an Ace (or trey or King) was indeed used as a burn card.

The kicker is, she'll say "but what if it *IS* a king"

"but we don't know that, but we can calculate it's likelyhood"

"but what if IT IS A KING AS A BURN CARD..."

... and around and around and around we go!

[eyes rolling] ....

[/ QUOTE ]

She seems to have an alright understanding of probability why don't you have her calculate the odds that the burn card is a king or any other card for that matter. By the time the math is worked out your odds for getting the next card you are looking for remain the same.

For the original problems, a suggestion similar to some posted already would be to take the deck of 50 and when after she agreed the odds for the top card being and ace at 1/25. Take the top card of the deck of the deck essentially making the deck one card. The odds shouldn't of changed just by changing the location of the top card.

[Dromar]

[ QUOTE ]

I tried showing her the deck face down in my hand, with two Aces removed. Then I ask her the odds of the top card being an Ace. 1/25 she replies. So far, so good.

I remove the bottom card of the deck. What are the odds now?? 2/49, she replies. D'OH!!!!!


[/ QUOTE ]

OK. If she believes that, then put the removed card on top of the deck and ask again. If she says 1/25, she's disagreeing with herself. If she says 0, she should realize that she's wrong.

Saying that the odds were 2/49 is akin to claiming that the removed card cannot be an ace. Therefore, if that card is put on top, she would have to reason there there is no chance that the top card is an ace. What might put the point across faster is if that card happened to be an ace.

In my experience, it's impossible to get someone who claims "it either is or it isn't" to understand probability. They say that the probability is either 100% or 0%. They don't understand the next level; the fact that it's 100% Ace with 4% probability, or 0% Ace with 96% probability, which simplifies to 4% chance that it's an Ace.

[elindauer]

You are confusing the situation by making the deck change overly complex. Rather than talking about "burning half the deck", you should start by convincing her that the probability of the top card being an ace doesn't change no matter what you do to the rest of the deck.


Start by taking the top card off the deck. Point to it. What are the odds it's an ace? 1 in 25 she says. Separate it from the deck. What are the odds? 1 in 25.

Now start manipulating the rest of the deck, but in a very simple way. Move a card from the top to the bottom. What are the odds now? Hopefully she'1l agree it's 1 in 25. Cut it. Shuffle it. How about now? Shuffle it. Put the deck in a paper bag. Now?

Your goal is to slowly remove one card from the deck and get her to say the odds have not changed. If she ever changes answers, make the steps smaller. Tearing a card makes it 2 in 25? ok, what if I just tear a corner? What if I tape it back together, but keep it separated from the deck?

And if that doesn't do it, well, how about a prop bet? [img]/images/graemlins/smile.gif[/img]

-Eric

[KUJustin]

Win the argument? Heck, just win all her money.

[jamzfive]

[ QUOTE ]
"but what if IT IS A KING AS A BURN CARD..."


[/ QUOTE ]

Maybe you can just go down this road.
There are two possibilities:
A) the card from the bottom of the deck is an Ace
B) the card from the bottom of the deck is not an Ace.

If the card from the bottom of the deck is an Ace (which she apparently realizes correctly is 1/25), then there is only one Ace left in the rest of the deck, making the odds the top card is an Ace 1/49 (which she'll likely grasp as well).
If the card from the bottom of the deck is not an ace (24/25), then the odds the top card is an Ace is 2/49.

Combining these odds (which is the next gap in understand that you may reach) gives you
(1/25)*(1/49)+(24/25)*(2/49)
which "miraculously" equals 1/25.

[TomBrooks]

[ QUOTE ]
Win the argument? Heck, just win all her money.

[/ QUOTE ]
Offer her 15:1 and go to town. That's a whopping 21% premium on the 12.5:1 she believes is the right odds and she should jump at it.